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  • Open Access

Reference-frame-independent quantum metrology

Satoya Imai1,2,3,4,*, Otfried Gühne4, and Géza Tóth5,6,7,8,9

  • *Contact author: satoyaimai@yahoo.co.jp
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Phys. Rev. Research 8, 013327 – Published 26 March, 2026

DOI: https://doi.org/10.1103/988w-6tpf

Abstract

How can we perform a metrological task if only limited control over a quantum system is given? Here, we present systematic methods for conducting nonlinear quantum metrology in scenarios lacking a common reference frame. Our approach involves preparing multiple copies of quantum systems and then performing local measurements with randomized observables. First, we derive the metrological precision using an error-propagation formula based solely on local unitary invariants, which are independent of the chosen basis. Next, we provide analytical expressions for the precision scaling in various examples of nonlinear metrology involving two-body interactions, like the one-axis twisting Hamiltonian. Finally, we analyze our results in the context of local decoherence and discuss its influences on the observed scaling.

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Phys. Rev. Research 8, 013327– Published 26 March, 2026
  • Received 25 November 2024
  • Accepted 2 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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